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JAMB Mathematics 2023 Paper

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Question : 29

Total: 80

Factorize:

16x^4 - y^4

$(2x - y)(2x + y)(4x^2 + y^2)$
$(2x + y)(2x + y)(4x^2 + y^2)$
$(2x - y)(2x - y)(4x^2 + y^2)$
$(2x - y)(2x + y)(4x^2 - y^2)$

Solution:

Concept:

Use the difference of two squares identity:

a^2 - b^2 = (a - b)(a + b)

.

Explanation:

Write the expression as a difference of squares:

16x^4 - y^4 = (4x^2)^2 - (y^2)^2

Apply the identity:

(4x^2 - y^2)(4x^2 + y^2)

Factor

4x^2 - y^2

again using the same identity:

4x^2 - y^2 = (2x)^2 - y^2 = (2x - y)(2x + y)

Therefore:

16x^4 - y^4 = (2x - y)(2x + y)(4x^2 + y^2)

Answer:

(2x - y)(2x + y)(4x^2 + y^2)

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